The invention is generally directed to servomechanical control. In particular, the present invention provides an arrangement for enhancing the degree of stiffness (S) of a servo-mechanical control.
DC servomotors are widely used in the field of automated equipment such as industrial robots, numerically controlled fabrication machines, and intelligent printers or plotters. In these applications, loads operated by the motor (for instance, the hand architecture of robots cutting or drilling tools, printer heads of office terminals, and rollers or press machines) should be held at a predetermined position after movement from the preceding position within a short period of time. It becomes necessary to control the amount of electric current supplied to the servomotor by continuously detecting the position of the load and its moving velocity. For this purpose, a servomotor with high degree or responsiveness to commands and with capability to move promptly and to stop precisely is necessary. In normal practice, current to the rotor is controlled for this purpose. The present invention provides a control arrangement utilizing a small-sized motor achieving high degree of stiffness.
In FIG. 1, a DC servomotor (M) is mechanically linked to drive a load (L). A motive force of rotation is produced by supplying electric current to a rotor of the motor located in a magnetic field. The torque of the motor t.sub.L is proportional to the rotor current (i.sub.R) and, therefore, expressed as in equation 1: EQU t.sub.L =K.sub.T .multidot.i.sub.R ( 1)
where K.sub.T is the ratio of torque to rotor current which is constant for a given motor.
When the moment of inertia of the load around the loading axis of the motor is J.sub.M, the relation between the angle (.theta.) of the load around the loading axis and time (t) is expressed in the following equation of motion: ##EQU2## where EQU J=J.sub.M +J.sub.L. (3)
From equation 2 it is understood that the rotation angle (.theta.) can be controlled by varying the current (i.sub.R) in the rotor of the DC servomotor (M). In the practical application of the motor with i.sub.R control, there are many methods for determining the value of i.sub.R necessary for rotating the load to the target angle (.theta..sub.c). A commonly used method of control is shown in FIG. 2.
Referring now to FIG. 2, motor (M) is mechanically linked to drive a load (L). An angle detector (A) determines the angular position .theta. of the load with respect to a three-dimensional coordinate axis of x, y and z (not shown). A servo-drive circuit (B) determines the rotor current (i.sub.R) by comparing the value of .theta. observed by the angle detector with the target angle (.theta..sub.c).
FIG. 3 is a block diagram of a servo-drive circuit. Motor M drives load L. An angle detector A provides a signal indicative of load angle .theta. and a velocity detector V provides a signal indicative of the derivative .theta. of the load angle.
A proportional amplifier 3 is utilized to convert signal .theta. to -.theta.. An adder 1 adds -.theta. to .theta..sub.c representing the target angle of the load. A proportional amplifier 4 multiplies (d.theta./dt), obtained from a velocity detector (V), by the velocity coefficient (-K.sub.V), and an adder 2 adds (.theta..sub.c =.theta.) to the resistance to motion, that is, the product of -K.sub.V and (d.theta./dt). A proportional amplifier 5 determines the product of the feedback coefficient (K.sub.F) and [(.theta..sub.c -.theta.)-K.sub.V .multidot.(d.theta./dt)] and thus i.sub.R is given in equation 4: ##EQU3## Equation of motion 5 is derived from equations 1, 2, and 4: ##EQU4## EQU T=.OMEGA..sub.o .multidot.t (8)
where .OMEGA..sub.o is a time coefficient.
FIG. 4 illustrates an example wherein .theta. is a step signal having a height H and having a leading edge a time T=0.
FIG. 5 shows a step-signal response, that is, shift of .theta.ov. time (T) according to equation 5. In the figure, D represents the brake coefficient, and three typical values, 1.0, 0.707, and 0.5, are shown. When D is small, the load passes far beyond the commanded angle (.theta..sub.c) and merges to the value ultimately after several fluctuations.
When D is large, .theta. does not exceed .theta..sub.c. However, it is not likely that .theta. approaches .theta..sub.c in a short period of time. The most optimum approach of .theta. to the commanded value (.theta..sub.c) will be achieved when D=1.0. When D=0.707, it allows a small amount of passage of .theta. beyond .theta..sub.c. The value of D can be selected as described depending on the conditions of approach of .theta. to the desired commanded value (.theta..sub.c). Thus, velocity coefficient (K.sub.V) and feedback coefficient (K.sub.F) can be determined in order to give the D value which is most preferable under the circumstances given.
In equation 7, K.sub.T and J are determined when a motor and load are specified. However, the values of K.sub.V and K.sub.F cannot be determined even when K.sub.T, J, and D are specified. Thus, another factor becomes necessary to determine the values of K.sub.V and K.sub.F. A concept of "stiffness" of the servomechanical control has been introduced. Stiffness (S) is defined in equation 9: EQU S=t.sub.s /(.theta..sub.c -.theta.) (9)
where t.sub.s is the force necessary to hold the load at a constant position of .theta. from .theta..sub.c when the load is subjected to a constant external force. It is obvious that the higher the degree of stiffness, the closer the load can be held to the commanded position. From equations 1 and 4, S can be expressed as in equation 10: EQU S=K.sub.F .multidot.K.sub.T ( 10)
To obtain a high degree of stiffness, feedback coefficient (K.sub.F) of the system must be large. However, an increase of K.sub.F causes an increase of the rotor current of the motor and tends to exceed the motor's rated current. Thus, the feedback coefficient (K.sub.F) and, consequently, the stiffness (S) of the system are limited by the maximum allowable electric current of the motor. Although it had been tried to use a limiter to avoid exceeding the rated current of the motor, it had been found that doing so reduced the current for braking, and that the load thus moved beyond the commanded angle and took longer to converge. Generally, DC servomotors for driving robot links are required to be compact and light in weight and responsive to requirements. Moreover, a high degree of stiffness, that is, capability to hold the load firmly at the determined position, is also a requisite of servomotors in a control system. The above requirements must be met when selecting the optimum servomotor for a control system.